#905599 (C++17) No.2433 Min Increasing Sequence

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問題	No.2433 Min Increasing Sequence
コンテスト
ユーザー	tokusakurai
提出日時	2023-08-18 22:18:39
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	58 ms / 2,000 ms
コード長	15,217 bytes
コンパイル時間	2,096 ms
コンパイル使用メモリ	200,560 KB
最終ジャッジ日時	2025-02-16 10:15:16
ジャッジサーバーID （参考情報）	judge4 / judge3
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ファイルパターン	結果
other	AC * 32
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

int pct(int x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename T>
void reorder(vector<T> &a, const vector<int> &ord) {
    int n = a.size();
    vector<T> b(n);
    for (int i = 0; i < n; i++) b[i] = a[ord[i]];
    swap(a, b);
}

template <typename T>
T floor(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? x / y : (x - y + 1) / y);
}

template <typename T>
T ceil(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? (x + y - 1) / y : x / y);
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(15);
    }
} io_setup;

constexpr int inf = (1 << 30) - 1;
constexpr ll INF = (1LL << 60) - 1;
// constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;

template <int mod>
struct Mod_Int {
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    static int get_mod() { return mod; }

    Mod_Int &operator+=(const Mod_Int &p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator-=(const Mod_Int &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator*=(const Mod_Int &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator/=(const Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator++() { return *this += Mod_Int(1); }

    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator--() { return *this -= Mod_Int(1); }

    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator-() const { return Mod_Int(-x); }

    Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }

    Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }

    Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }

    Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }

    bool operator==(const Mod_Int &p) const { return x == p.x; }

    bool operator!=(const Mod_Int &p) const { return x != p.x; }

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }

    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }

    friend istream &operator>>(istream &is, Mod_Int &p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

using mint = Mod_Int<MOD>;

template <typename Monoid>
struct Segment_Tree {
    using M = typename Monoid::V;
    int n, m;
    vector<M> seg;

    // f(f(a,b),c) = f(a,f(b,c)), f(e1,a) = f(a,e1) = a

    Segment_Tree(const vector<M> &v) : n(v.size()) {
        m = 1;
        while (m < n) m <<= 1;
        seg.assign(2 * m, Monoid::id);
        copy(begin(v), end(v), begin(seg) + m);
        build();
    }

    Segment_Tree(int n, M x = Monoid::id) : Segment_Tree(vector<M>(n, x)) {}

    void set(int i, const M &x) { seg[m + i] = x; }

    void build() {
        for (int i = m - 1; i > 0; i--) seg[i] = Monoid::merge(seg[2 * i], seg[2 * i + 1]);
    }

    void update(int i, const M &x, bool apply = false) {
        seg[i + m] = apply ? Monoid::merge(seg[i + m], x) : x;
        i += m;
        while (i >>= 1) seg[i] = Monoid::merge(seg[2 * i], seg[2 * i + 1]);
    }

    M query(int l, int r) const {
        l = max(l, 0), r = min(r, n);
        M L = Monoid::id, R = Monoid::id;
        l += m, r += m;
        while (l < r) {
            if (l & 1) L = Monoid::merge(L, seg[l++]);
            if (r & 1) R = Monoid::merge(seg[--r], R);
            l >>= 1, r >>= 1;
        }
        return Monoid::merge(L, R);
    }

    M operator[](int i) const { return seg[m + i]; }

    template <typename C>
    int find_subtree(int i, const C &check, M &x, int type) const {
        while (i < m) {
            M nxt = type ? Monoid::merge(seg[2 * i + type], x) : Monoid::merge(x, seg[2 * i + type]);
            if (check(nxt)) {
                i = 2 * i + type;
            } else {
                x = nxt;
                i = 2 * i + (type ^ 1);
            }
        }
        return i - m;
    }

    // check(区間 [l,r] での演算結果) を満たす最小の r (存在しなければ n)
    template <typename C>
    int find_first(int l, const C &check) const {
        M L = Monoid::id;
        int a = l + m, b = 2 * m;
        while (a < b) {
            if (a & 1) {
                M nxt = Monoid::merge(L, seg[a]);
                if (check(nxt)) return find_subtree(a, check, L, 0);
                L = nxt;
                a++;
            }
            a >>= 1, b >>= 1;
        }
        return n;
    }

    // check((区間 [l,r) での演算結果)) を満たす最大の l (存在しなければ -1)
    template <typename C>
    int find_last(int r, const C &check) const {
        M R = Monoid::id;
        int a = m, b = r + m;
        while (a < b) {
            if ((b & 1) || a == 1) {
                M nxt = Monoid::merge(seg[--b], R);
                if (check(nxt)) return find_subtree(b, check, R, 1);
                R = nxt;
            }
            a >>= 1, b >>= 1;
        }
        return -1;
    }
};

// sum
template <typename T>
struct Plus_Monoid {
    using V = T;
    static constexpr V merge(const V &a, const V &b) { return a + b; };
    static const V id;
};

template <typename T>
const T Plus_Monoid<T>::id = 0;

// prod
template <typename T>
struct Product_Monoid {
    using V = T;
    static constexpr V merge(const V &a, const V &b) { return a * b; };
    static const V id;
};

template <typename T>
const T Product_Monoid<T>::id = 1;

// min
template <typename T>
struct Min_Monoid {
    using V = T;
    static constexpr V merge(const V &a, const V &b) { return min(a, b); };
    static const V id;
};

template <typename T>
constexpr T Min_Monoid<T>::id = numeric_limits<T>::max() / 2;

// max
template <typename T>
struct Max_Monoid {
    using V = T;
    static constexpr V merge(V a, V b) { return max(a, b); };
    static const V id;
};

template <typename T>
constexpr T Max_Monoid<T>::id = -(numeric_limits<T>::max() / 2);

// 代入
template <typename T>
struct Update_Monoid {
    using V = T;
    static constexpr V merge(const V &a, const V &b) {
        if (a == id) return b;
        if (b == id) return a;
        return b;
    }
    static const V id;
};

template <typename T>
constexpr T Update_Monoid<T>::id = numeric_limits<T>::max();

// min count (T：最大値の型、S：個数の型)
template <typename T, typename S>
struct Min_Count_Monoid {
    using V = pair<T, S>;
    static constexpr V merge(const V &a, const V &b) {
        if (a.first < b.first) return a;
        if (a.first > b.first) return b;
        return V(a.first, a.second + b.second);
    }
    static const V id;
};

template <typename T, typename S>
constexpr pair<T, S> Min_Count_Monoid<T, S>::id = make_pair(numeric_limits<T>::max() / 2, 0);

// max count (T：最大値の型、S：個数の型)
template <typename T, typename S>
struct Max_Count_Monoid {
    using V = pair<T, S>;
    static constexpr V merge(const V &a, const V &b) {
        if (a.first > b.first) return a;
        if (a.first < b.first) return b;
        return V(a.first, a.second + b.second);
    }
    static const V id;
};

template <typename T, typename S>
constexpr pair<T, S> Max_Count_Monoid<T, S>::id = make_pair(-(numeric_limits<T>::max() / 2), 0);

// 一次関数 ax+b の合成 (左から順に作用)
template <typename T>
struct Affine_Monoid {
    using V = pair<T, T>;
    static constexpr V merge(const V &a, const V &b) { return V(a.first * b.first, a.second * b.first + b.second); };
    static const V id;
};

template <typename T>
const pair<T, T> Affine_Monoid<T>::id = make_pair(1, 0);

// モノイドの直積
template <typename Monoid_1, typename Monoid_2>
struct Cartesian_Product_Monoid {
    using V1 = typename Monoid_1::V;
    using V2 = typename Monoid_2::V;
    using V = pair<V1, V2>;
    static constexpr V merge(const V &a, const V &b) { return V(Monoid_1::merge(a.first, b.first), Monoid_2::merge(a.second, b.second)); }
    static const V id;
};

template <typename Monoid_1, typename Monoid_2>
const pair<typename Monoid_1::V, typename Monoid_2::V> Cartesian_Product_Monoid<Monoid_1, Monoid_2>::id = make_pair(Monoid_1::id, Monoid_2::id);

// range add range min
template <typename T>
struct Min_Plus_Acted_Monoid {
    using Monoid = Min_Monoid<T>;
    using Operator = Plus_Monoid<T>;
    using M = T;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return a + b; };
};

// range add range max
template <typename T>
struct Max_Plus_Acted_Monoid {
    using Monoid = Max_Monoid<T>;
    using Operator = Plus_Monoid<T>;
    using M = T;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return a + b; };
};

// range add range min count (T：最小値の型、S：個数の型)
template <typename T, typename S>
struct Min_Count_Add_Acted_Monoid {
    using Monoid = Min_Count_Monoid<T, S>;
    using Operator = Plus_Monoid<T>;
    using M = pair<T, S>;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return make_pair(a.first + b, a.second); };
};

// range add range max count (T：最大値の型、S：個数の型)
template <typename T, typename S>
struct Max_Count_Add_Acted_Monoid {
    using Monoid = Max_Count_Monoid<T, S>;
    using Operator = Plus_Monoid<T>;
    using M = pair<T, S>;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return make_pair(a.first + b, a.second); };
};

// range add range sum
template <typename T>
struct Plus_Plus_Acted_Monoid {
    using Monoid = Cartesian_Product_Monoid<Plus_Monoid<T>, Plus_Monoid<int>>;
    using Operator = Plus_Monoid<T>;
    using M = pair<T, int>;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return M(a.first + b * a.second, a.second); }
};

// range update range sum
template <typename T>
struct Plus_Update_Acted_Monoid {
    using Monoid = Cartesian_Product_Monoid<Plus_Monoid<T>, Plus_Monoid<int>>;
    using Operator = Update_Monoid<T>;
    using M = pair<T, int>;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return b == Operator::id ? a : M(b * a.second, a.second); }
};

// range update range min
template <typename T>
struct Min_Update_Acted_Monoid {
    using Monoid = Min_Monoid<T>;
    using Operator = Update_Monoid<T>;
    using M = T;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return b == Operator::id ? a : b; }
};

// range update range max
template <typename T>
struct Max_Update_Acted_Monoid {
    using Monoid = Max_Monoid<T>;
    using Operator = Update_Monoid<T>;
    using M = T;
    using O = T;
    static constexpr M merge(const M &a, const O &b) { return b == Operator::id ? a : b; }
};

// range affine range sum
template <typename T>
struct Plus_Affine_Acted_Monoid {
    using Monoid = Cartesian_Product_Monoid<Plus_Monoid<T>, Plus_Monoid<T>>;
    using Operator = Affine_Monoid<T>;
    using M = pair<T, T>;
    using O = pair<T, T>;
    static constexpr M merge(const M &a, const O &b) { return M(b.first * a.first + b.second * a.second, a.second); };
};

void solve() {
    int N;
    cin >> N;

    vector<int> a(N);
    rep(i, N) cin >> a[i];

    if (N == 1) {
        cout << "1\n";
        return;
    }

    Segment_Tree<Min_Monoid<int>> seg(a);

    vector<mint> dp(N + 1, 0);
    dp[0] = 1;

    rep(i, N) {
        if (i >= 2) dp[i] += dp[i - 1];
        int x = seg.query(i, N);
        auto c = [&](int y) { return y <= x; };
        int j = seg.find_first(i, c);
        dp[j + 1] += dp[i];
    }
    dp[N] += dp[N - 1];

    // print(dp);

    cout << dp[N] << '\n';
}

int main() {
    int T = 1;
    // cin >> T;
    while (T--) solve();
}
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